Results 1 to 5 of 5

Math Help - Inequality Application

  1. #1
    Member
    Joined
    Dec 2007
    From
    Georgia
    Posts
    85

    Inequality Application

    A charter airline finds that on its Saturday flights from Philadelphia to London, all 120 seats will be sold if the ticket price is $200. However, for each $3 increase in ticket price, the number of seats sold decreases by one.

    a) Find a formula for the number of seats sold if the ticket price is P dollars.
    The answer for a is -\frac{1}{3}P + \frac{560}{3}. However, I do not see how they arrived at that answer. Any help will be greatly appreciated.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by mathgeek777 View Post
    The answer for a is -\frac{1}{3}P + \frac{560}{3}. However, I do not see how they arrived at that answer. Any help will be greatly appreciated.
    do you realize that we have a linear relationship between the number of seats filled and the ticket price? since each changes at a constant rate with respect to each other.

    lets think of this graphically so that you get the idea. we want a function of price, so put that on the x-axis. the number of seats on the y-axis. now, plot a few points:

    \begin{array}{c|c} S & P \\ \hline 120 & 200 \\ 119 & 203 \\ 118 & 206 \\ . & . \\ . & . \\ . & . \end{array}

    S is the number of seats, P is the price. S goes down by 1 when P goes up by 3

    all we need to do is find the straight line that passes through these points. can you do that?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Dec 2007
    From
    Georgia
    Posts
    85
    Ok. I see where the -\frac{1}{3} came from, but i still don't know how you get \frac{560}{3)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by mathgeek777 View Post
    Ok. I see where the -\frac{1}{3} came from, but i still don't know how you get \frac{560}{3}
    the equation of a line in the slope-intercept form is y = mx + b, where m is the slope and b, is the y-intercept.

    given any two points on the line, (x_1, y_1) and (x_2,y_2), we can find the equation of the line as follows:

    m = \frac {y_2 - y_1}{x_2 - x_1}

    By the point-slope form, plug in the values of m, x_1 and y_1 into:

    y - y_1 = m(x - x_1)

    and solve for y to get it into the slope-intercept form.

    alternatively, we could plug the points into y = mx + b and solve for b, since it would be the only unknown at this point

    here of course, your y is S and your x is P
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,738
    Thanks
    644
    Hello, mathgeek777!

    A charter airline finds that on its Saturday flights from Philadelphia to London,
    all 120 seats will be sold if the ticket price is $200.
    However, for each $3 increase in ticket price, the number of seats sold decreases by one.

    a) Find a formula for the number of seats sold if the ticket price is P dollars.

    The answer is: -\frac{1}{3}P + \frac{560}{3}

    Let x = number of $3-increases in the price of a ticket.

    Then the price is: . P \:=\:200 + 3<br />
x\quad\Rightarrow\quad x \:=\:\frac{P - 200}{3}\;\;{\color{blue}[1]}

    . . and the number of seats sold is: . S \;=\;120 - x\;\;{\color{blue}[2]}


    Substitute [1] into [2]: . S \;=\;120 - \frac{P-200}{3} \;=\;\frac{360}{3} - \frac{P-200}{3} \;=\;\frac{-P + 560}{3}

    Therefore: . S \;=\;-\frac{1}{3}P + \frac{560}{3}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Application of Chebyshev's inequality
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: December 6th 2010, 11:50 AM
  2. Application of Chebshev's Inequality
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 27th 2010, 11:06 PM
  3. complex: question with application of Cauchy's Inequality
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: December 1st 2009, 08:09 PM
  4. Inequality Application
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: February 4th 2009, 09:09 PM
  5. Replies: 1
    Last Post: October 9th 2008, 03:17 AM

Search Tags


/mathhelpforum @mathhelpforum